Well, there is already a couple of historical spanners in the works with Rome deciding that they want to go SPQR again and conquering/allying with the entire Italian pennisula and somehow coming into possession of Constantinople (better have an impressive story to that one General Havoc), and the Normans never losing control of the Kingdom of Sicily to the Holy Roman Empire and later the Kingdom of Aragon. This throws all sorts of political weirdness into the batch, especially since the Sicilians control Tunisia which means they will have a significant minority of Muslims under their control which means that having a weak pope is to their advantage to keep anyone from poking them over the whole 'heresy of indifferentiation' thing.That sounds exactly like the historical schism. That issue was resolved in 1418, what rationale is there for the resolution to fail in this scenario? If the Romans didn't kick the Pope out entirely, I don't see how the schism wouldn't have been resolved. Pretty much every power preferred a single pope, which is why the whole matter did not last and eventually they went back to the one. The extra Pope won't last without state support, and such will be withdrawn once a majority has settled on one, as was the case historically.
Actually, it might be a good time to start discussing some of the mutual backstory. The big point of divergence for the Norman Sicilians is that during the Norman conquest they discovered a cache of Archimedes writings, prototypes, and models outside Syracuse during their conquest of the island. This wealth of knowledge brought not just improvements in technology, but brought in Byzantine (and later even Islamic!) scholars interested in the ancient works, and with them brought increased trade, which the Norman kings encouraged, leading to great prosperity that they leveraged for all it was worth. They quickly had a large navy to protect their merchant ships, which let them actually hold the coast of Tunisia despite repeatedly getting kicked out of the interior by various jihads. Tunisia proved lucrative when combined with some of the technology developed from Archimedes work.
The early influx of classical work probably helped remind the people of Rome of the role they once played and contributed to their reemergence as the power from a thousand years prior.